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一类非齐次障碍问题很弱解的正则性 被引量：7

Regularity of the Very Weak Solutions for Nonhomogeneous Obstacle Problems
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摘要 本文研究形如divA(x,u)=B(x,u)的非齐次椭圆算子的障碍问题,给出了二阶非齐次障碍问题解的定义,并利用Hodge分解,获得非齐次障碍问题的解及其导数的一些性质. This paper studies the obstacle problems associated with two order nonhomogeneous elliptic equation divA（x, △u） = B（x, △u） ,gives the definition of solutions of second order degenerate nonhomogeneous obstacle problems,and making use of the Hodge de- composition and others,acquire some properties of these solutions and their derivative.
作者 佟玉霞 谷建涛 曹建亮
机构地区 河北理工大学理学院
出处 《应用数学》 CSCD 北大核心 2008年第1期185-192,共8页 Mathematica Applicata
基金 河北省教育厅博士基金资助项目(B2004103)
关键词 障碍问题 椭圆算子 HODGE分解 Obstacle problem Elliptic equation Hodge decomposition
分类号 O175.23 [理学—基础数学]
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参考文献3

二级参考文献22

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共引文献31

同被引文献19

  • 1谢素英,田欢.一类拟线性椭圆型方程弱解关于区域的稳定性[J].应用数学,2009,22(3):566-570. 被引量：1
  • 2Gao Hongya,Li Juan,Deng Yanjun.EXTREMUM PRINCIPLE FOR VERY WEAK SOLUTIONS OF A-HARMONIC EQUATION[J].Journal of Partial Differential Equations,2005,18(3):235-240. 被引量：2
  • 3佟玉霞,徐秀娟,朱新华,王新春.A-调和方程弱解的双权Caccioppoli型不等式[J].数学的实践与认识,2007,37(3):130-134. 被引量：4
  • 4Iwaniec T, Sbordone C. Weak minima of variational integrals[J]. J Reine Angew Math, 1994, 454: 143-161.
  • 5Greco L, Iwaniec T, Sbordone C. Inverting the p-harmonic operator[J]. Manuscripta Math, 1997, 92(2): 249-258.
  • 6Bojarski B, Iwaniec T. Analytical foundation of the theory of quasiconformal mappings in Rn[J]. Ann Acad Sci Fenn Math Set A, 1993, 8: 257-324.
  • 7Li Gongbao, Martio O. Stability of solutions of varying degenerate elliptic equations[J]. Indiana Univ Math J, 1998, 47(3): 873-891.
  • 8Giaquinta M. Multiple Integrals in the Calculus of Variations and Nonliear Elliptic Systems[M]. Princeton: Princeton University Press, 1983.
  • 9Elcrat A, Meyers N. Some results on regularity for non-linear elliptic systems and quasiregular functions[J]. Duke Math J, 1975, 42: 121-136.
  • 10T Iwaniec T, Migliaccio L, Nania L, et al. Integrability and removability results for quasiregular mappings in high dimensions[J]. Math Scand, 1994, 75: 263-279.

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二级引证文献8

应用数学
2008年 第1期

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